Sample Size for Pearson's Correlation

 

Menu location: Analysis_Sample Size_Correlation.

 

This function gives you the minimum number of pairs of subjects needed to detect a true difference in Pearson's correlation coefficient between the null (usually 0) and alternative hypothesis levels with power POWER and two sided type I error probability ALPHA (Stuart and Ord, 1994; Draper and Smith, 1998).

 

Information required

 

Practical issues

 

Technical validation

The sample size estimation uses Fisher's classic z-transformation to normalize the distribution of Pearson's correlation coefficient:

 

This gives rise to the usual test for an observed correlation coefficient (r1) to be tested for its difference from a pre-defined reference value (r0, often 0), and from this the power and sample size (n) can be determined:

 

StatsDirect makes an initial estimate of n as:

 

StatsDirect then finds the value of n that satisfies the following power (1-β) equation:

-where norm is the area under the standard normal distribution curve.

 

The precise value of n is rounded up to the closest integer in the results given by StatsDirect.

 

 

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